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تسجيل مستخدم جديدComputing L-series of hyperelliptic curves
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We discuss the computation of coefficients of the L-series associated to a hyperelliptic curve over Q of genus at most 3, using point counting, generic group algorithms, and p-adic methods.
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We analyze the distribution of unitarized L-polynomials Lp(T) (as p varies) obtained from a hyperelliptic curve of genus g <= 3 defined over Q. In the generic case, we find experimental agreement with a predicted correspondence (based on the Katz-Sar
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We give an explicit description of the stable reduction of superelliptic curves of the form $y^n=f(x)$ at primes $p$ whose residue characteristic is prime to the exponent $n$. We then use this description to compute the local $L$-factor of the curve and the exponent of conductor at $p$.
Given a hyperelliptic curve $C$ of genus $g$ over a number field $K$ and a Weierstrass model $mathscr{C}$ of $C$ over the ring of integers ${mathcal O}_K$ (i.e. the hyperelliptic involution of $C$ extends to $mathscr{C}$ and the quotient is a smooth
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Let $K$ be a field of characteristic different from $2$, $bar{K}$ its algebraic closure. Let $n ge 3$ be an odd prime such that $2$ is a primitive root modulo $n$. Let $f(x)$ and $h(x)$ be degree $n$ polynomials with coefficients in $K$ and without r
epeated roots. Let us consider genus $(n-1)/2$ hyperelliptic curves $C_f: y^2=f(x)$ and $C_h: y^2=h(x)$, and their jacobians $J(C_f)$ and $J(C_h)$, which are $(n-1)/2$-dimensional abelian varieties defined over $K$. Suppose that one of the polynomials is irreducible and the other reducible. We prove that if $J(C_f)$ and $J(C_h)$ are isogenous over $bar{K}$ then both jacobians are abelian varieties of CM type with multiplication by the field of $n$th roots of $1$.
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